What is the integral from 1 to infinity of xe^{-x} ?

The integral from 1 to infinity of xe^{-x} is 2/e

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integral from 1 to infinity of xe^{-x}

\int_{1}^{\infty} x e^{- x} d x

\frac{2}{e}

Decimal Notation

0.73575 \dots

Solution steps

\int_{1}^{\infty} x e^{- x} d x

Compute the indefinite integral:

\int x e^{- x} d x = - e^{- x} x - e^{- x} + C

Compute the boundaries:

\int_{1}^{\infty} x e^{- x} d x = 0 - (- \frac{2}{e})

= 0 - (- \frac{2}{e})

Simplify

= \frac{2}{e}

\frac{d}{d x} (- \frac{1}{5} (x^{- 5} - x^{10}))

\frac{\partial}{\partial v} (u \cdot sin (v))

x \to (0) + lim (\frac{ln ( x )}{x})

f (x) = ∣ x - 2 ∣

x \to - 1 lim (\frac{x + 3}{x + 1})

What is the integral from 1 to infinity of xe^{-x} ?
The integral from 1 to infinity of xe^{-x} is 2/e